This is a research topic widely worked on for a number of years. The scientific data definitely do back up the mentioned observations. Simply put, it has a lot to do with the difference in nature of upbringing by parents in matrimonial union vs separated ones. The very obvious reasons we can all pick out include: more extreme displays of negative interactions (e.g. physical and verbal abuse), amount of attention received by child, etc. It is extremely important, however, to note that the display of the above characteristics and the validity of the matrimonial union are not mutually exclusive. Children from "complete families" may not necessarily get more attention than a child raised by a single mom, for example.
Proceeding with the generalisations, psychologists that have done extensive research on adolescent behaviour would deem family as an important role model for the child, in terms of what they would then perceive to be normal and acceptable familial interaction. This is probably why the vicious cycle of domestic abuse is hard to break. To a more socially developed person at a healthy level, abuse would naturally not be deemed acceptable.
Also, the adults in the family (usually refers to the parents) are usually assumed to be emotionally mature and thus able to nurture their children to develop applicable social skills in the future. If such is not the case, then the child will likely lack those skills, leading to the aforementioned social problems.
The possibility that divorced parents give their child less attention also should not be ignored. The common explanation is that divorced parents are separated and hence every time a child is receiving attention, he/she is receiving it from only one parent at a time, as opposed to two parents. In more extreme cases of single-upbringing, the child only knows of one parent's love. Again, another generalisation, but it helps to explain how lesser attention can possibly affect the confidence levels of such children, especially when they are at the age where they compare their circumstances with other children. The exclusivity may result in further impediment of their emotional growth, resulting in lowered rates of social emotional growth, which is linked to the said social problems.
Of course, I sound like I'm implying children with divorced parents will definitely have it tough, and that those in complete families will be safe from the same problems. Just a disclaimer that I understand that people divorce for many reasons other than those implying that they lack certain social skills. It is a bold generalisation that perhaps divorce brings about a difference in type and number of skills taught to the child compared to an average child from a complete family. It is thus, such differences that generate varying levels of disparity between children from the two ends of the spectrum. Just as statistics prove that not all children from such familial circumstances face the same social problems to the same degree, the converse of my generalisations will show why it is the case.